| /*- |
| * SPDX-License-Identifier: BSD-2-Clause-FreeBSD |
| * |
| * Copyright (c) 2007-2008 David Schultz <das@FreeBSD.ORG> |
| * All rights reserved. |
| * |
| * Redistribution and use in source and binary forms, with or without |
| * modification, are permitted provided that the following conditions |
| * are met: |
| * 1. Redistributions of source code must retain the above copyright |
| * notice, this list of conditions and the following disclaimer. |
| * 2. Redistributions in binary form must reproduce the above copyright |
| * notice, this list of conditions and the following disclaimer in the |
| * documentation and/or other materials provided with the distribution. |
| * |
| * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND |
| * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE |
| * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE |
| * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE |
| * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL |
| * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS |
| * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) |
| * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT |
| * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY |
| * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF |
| * SUCH DAMAGE. |
| */ |
| |
| #include <sys/cdefs.h> |
| __FBSDID("$FreeBSD$"); |
| |
| #include <complex.h> |
| #include <float.h> |
| #include <math.h> |
| |
| #include "math_private.h" |
| |
| /* |
| * Several thresholds require a 15-bit exponent and also the usual bias. |
| * s_logl.c and e_hypotl have less hard-coding but end up requiring the |
| * same for the exponent and more for the mantissa. |
| */ |
| #if LDBL_MAX_EXP != 0x4000 |
| #error "Unsupported long double format" |
| #endif |
| |
| /* |
| * Overflow must be avoided for components >= LDBL_MAX / (1 + sqrt(2)). |
| * The precise threshold is nontrivial to determine and spell, so use a |
| * lower threshold of approximaely LDBL_MAX / 4, and don't use LDBL_MAX |
| * to spell this since LDBL_MAX is broken on i386 (it overflows in 53-bit |
| * precision). |
| */ |
| #define THRESH 0x1p16382L |
| |
| long double complex |
| csqrtl(long double complex z) |
| { |
| long double complex result; |
| long double a, b, rx, ry, scale, t; |
| |
| a = creall(z); |
| b = cimagl(z); |
| |
| /* Handle special cases. */ |
| if (z == 0) |
| return (CMPLXL(0, b)); |
| if (isinf(b)) |
| return (CMPLXL(INFINITY, b)); |
| if (isnan(a)) { |
| t = (b - b) / (b - b); /* raise invalid if b is not a NaN */ |
| return (CMPLXL(a + 0.0L + t, a + 0.0L + t)); /* NaN + NaN i */ |
| } |
| if (isinf(a)) { |
| /* |
| * csqrt(inf + NaN i) = inf + NaN i |
| * csqrt(inf + y i) = inf + 0 i |
| * csqrt(-inf + NaN i) = NaN +- inf i |
| * csqrt(-inf + y i) = 0 + inf i |
| */ |
| if (signbit(a)) |
| return (CMPLXL(fabsl(b - b), copysignl(a, b))); |
| else |
| return (CMPLXL(a, copysignl(b - b, b))); |
| } |
| if (isnan(b)) { |
| t = (a - a) / (a - a); /* raise invalid */ |
| return (CMPLXL(b + 0.0L + t, b + 0.0L + t)); /* NaN + NaN i */ |
| } |
| |
| /* Scale to avoid overflow. */ |
| if (fabsl(a) >= THRESH || fabsl(b) >= THRESH) { |
| /* |
| * Don't scale a or b if this might give (spurious) |
| * underflow. Then the unscaled value is an equivalent |
| * infinitesmal (or 0). |
| */ |
| if (fabsl(a) >= 0x1p-16380L) |
| a *= 0.25; |
| if (fabsl(b) >= 0x1p-16380L) |
| b *= 0.25; |
| scale = 2; |
| } else { |
| scale = 1; |
| } |
| |
| /* Scale to reduce inaccuracies when both components are denormal. */ |
| if (fabsl(a) < 0x1p-16382L && fabsl(b) < 0x1p-16382L) { |
| a *= 0x1p64; |
| b *= 0x1p64; |
| scale = 0x1p-32; |
| } |
| |
| /* Algorithm 312, CACM vol 10, Oct 1967. */ |
| if (a >= 0) { |
| t = sqrtl((a + hypotl(a, b)) * 0.5); |
| rx = scale * t; |
| ry = scale * b / (2 * t); |
| } else { |
| t = sqrtl((-a + hypotl(a, b)) * 0.5); |
| rx = scale * fabsl(b) / (2 * t); |
| ry = copysignl(scale * t, b); |
| } |
| |
| return (CMPLXL(rx, ry)); |
| } |